When they began working together in 1956. The buttoned-up Dr. William H. Masters, who was on the obstetrics-gynecology faculty of Washington University, provided the academic qualifications for the study, and Johnson, a twice-divorced former country singer, offered the practical aspects. She was a woman comfortable in her body who enjoyed sex, and she is the woman Caplan portrays in the new television series “Masters of Sex.”

The fascinating new Showtime drama premieres Sunday, with Welsh actor Michael Sheen as Masters. The series is based on Thomas Maier’s biography of the same name, which looked at the couple’s more than 40-year relationship. It was an unusual partnership to say the least, one that included clinical sex as part of their research, marriage and divorce.

The series — which involves the early years of the researchers’ lives — is something of a challenge for the premium cable network.

Can you make a show that features sex that isn’t salacious? Can you do research about sex without making it titillating?

It almost mirrors Masters’ and Johnson’s own dilemma.

While, biologist Alfred Kinsey’s earlier research on sexuality helped pave the way for academia’s interest in the subject, the majority of it came from personal accounts. Masters, though, wanted measurements — literally. So in 1955, with permission of the university and the local archbishop, he began to conduct a study of female sexuality in brothels. Picture a man in lab coat and bow tie peeking through holes in the wall or closets to watch prostitutes with their clients. Doesn’t sound very scientific — more like a peeping Tom.

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Like the overwhelming majority of men (even today), Masters was rather clueless about women. Then, one day, Masters learned to his surprise from one of his female subjects that women fake orgasms for a variety of reasons. She went on to tell him he didn’t understand female sexuality at all and needed someone who intimately knew the area as a research partner.

Johnson, who was the source of much of Maier’s book, was an unusual woman for the time.

“She definitely knew how to use her sexuality to get what she wanted,” Caplan says. “But unlike a lot of women, she genuinely enjoyed sex at a time when it wasn’t necessarily OK for a woman to openly and publicly be that way.”

A secretary in the ob-gyn clinic with two children and no college degree when she met Masters, the resourceful Johnson helped take Masters’ research to places he couldn’t imagine.

The pair began observing individuals (many of them volunteers from the university) masturbating and couples having sex in a clinical environment. They also began to quantify the subjects’ physiological reactions, recording heart rates and brain activity. Masters even put a tiny camera in an artificial phallus in order to watch what happens during female sexual arousal.

Although he was married at the time, Masters suggested that Johnson — who was seeing someone else — have sex with him as part of their research. Maier’s book and the series suggest that she would have been replaced had she not agreed.

“Masters of Sex” writer and executive producer Michelle Ashford says the couple’s “lives were so complicated and interesting” that the series needed to invent very little to create drama — and comedy — for the series.

“I think tone is very important with this show,” says the 44-year-old classically trained Sheen (“Frost/Nixon,” “The Queen”). “It’s going between images of nudity and sexuality that would be seen in conventional terms as kind of sexually exciting. But it’s up against things that are much more medical and gynecological. Notoriously, we as a culture and a society have some issues with that kind of thing.”

Since she is known more for comedies such as “Mean Girls,” “Party Down,” and an arc on “The New Girl,” the 31-year-old Caplan may seem an unlikely choice to play Johnson.

“I realized I was carving out a niche of the comedic acerbic girl,” says the Los Angeles native. “But I’ve always been proud of the fact that I’ve generally played strong women. Still, when I started out as an actress I wanted to do as many things as possible and thought myself capable of doing more.”

Director John Madden (“Shakespeare in Love,” “The Best Exotic Marigold Hotel”), who signed on to the project to be an executive producer and direct the pilot episode, saw her potential.

“He seemed to believe I was ready for the role even before I knew myself,” says Caplan.

Though sexuality is central to the show, executive producer Sarah Timberman insists there are no gratuitous sex scenes.

“The aim was to tell a story through sex scenes,” she says. “We never want to feel that the show just stops cold so that people can have sex.”

Still, there is a lot of nudity on the set for both men and women. Caplan says she had done a nude scene once before.

“I thought it was going to be really getting scary,” she says, “but I walked away with the complete opposite experience. I felt empowered and fully in control of my own body.”

The actors — like the researchers — grew accustomed to the nudity after a while.

“I never thought I would get used to having a naked woman in front of me masturbating, to the point where I would almost not notice it,” Sheen says.

While sex sells, will a series that’s built around sex sell?

“Interestingly, people are pulling back on the subject as sexual imagery is everywhere in our lives,” notes Caplan. “With every website you click on and every bag of chips somebody’s trying to sell, there are usually some elements of sex, and yet people’s desires to have a frank, open conversation about it seem to be going backwards.”

Of course, we love to gaze backwards. Like “Mad Men,” that late-1950s look in fashion and style is featured on “Masters of Sex.” Caplan, herself, wears a selection of poodle skirts and insisted on wearing a girdle and stockings on the set.